Second-order Lagrangians admitting a second-order Hamilton-Cartan formalism

Abstract

The Poincare-Cartan (PC) form of a Lagrangian on the bundle J2 = J2(N,M) is, as a general rule, defined on J3 thus leading to a non-equivalence between Euler-Lagrange and Hamilton-Cartan equations. This naturally leads to the problem of determining what Lagrangians have a PC form projectable onto J2, as they will then admit a second-order Hamiltonian formalism. There are specific examples of this phenomenon in field theory. This paper provides an explicit classification of such Lagrangians.